SURGIN: SURrogate-guided Generative INversion for subsurface multiphase flow with quantified uncertainty

Abstract: We present a direct inverse modeling method named SURGIN, a SURrogate-guided Generative INversion framework tailed for subsurface multiphase flow data assimilation. Unlike existing inversion methods that require adaptation for each new observational configuration, SURGIN features a zero-shot conditional generation capability, enabling real-time assimilation of unseen monitoring data without task-specific retraining. Specifically, SURGIN synergistically integrates a U-Net enhanced Fourier Neural Operator (U-FNO) surrogate with a score-based generative model (SGM), framing the conditional generation as a surrogate prediction-guidance process in a Bayesian perspective. Instead of directly learning the conditional generation of geological parameters, an unconditional SGM is first pretrained in a self-supervised manner to capture the geological prior, after which posterior sampling is performed by leveraging a differentiable U-FNO surrogate to enable efficient forward evaluations conditioned on unseen observations. Extensive numerical experiments demonstrate SURGIN's capability to decently infer heterogeneous geological fields and predict spatiotemporal flow dynamics with quantified uncertainty across diverse measurement settings. By unifying generative learning with surrogate-guided Bayesian inference, SURGIN establishes a new paradigm for inverse modeling and uncertainty quantification in parametric functional spaces.